4D Spatiotemporal Formulation for Convection-Diffusion Problems
Analysis
This paper introduces a novel 4D spatiotemporal formulation for solving time-dependent convection-diffusion problems. By treating time as a spatial dimension, the authors reformulate the problem, leveraging exterior calculus and the Hodge-Laplacian operator. The approach aims to preserve physical structures and constraints, leading to a more robust and potentially accurate solution method. The use of a 4D framework and the incorporation of physical principles are the key strengths.
Key Takeaways
- •Proposes a 4D spatiotemporal formulation for convection-diffusion problems.
- •Utilizes exterior calculus and the Hodge-Laplacian operator.
- •Aims to preserve physical structures and constraints.
- •Introduces an exponentially-fitted 4D spatiotemporal flux operator.
- •Proves convergence to the original time-dependent model.
Reference
“The resulting formulation is based on a 4D Hodge-Laplacian operator with a spatiotemporal diffusion tensor and convection field, augmented by a small temporal perturbation to ensure nondegeneracy.”